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<p><code>#include &lt;<a class="el" href="group__elem_8h_source.html">group_elem.h</a>&gt;</code></p>
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Inheritance diagram for cGroupElem&lt; T, BinaryOp &gt;:</div>
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Collaboration diagram for cGroupElem&lt; T, BinaryOp &gt;:</div>
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Public Types</h2></td></tr>
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typedef <a class="el" href="classcGroupElem.html">cGroupElem</a>&lt; T, BinaryOp &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>SelfType</b></td></tr>
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Public Member Functions</h2></td></tr>
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&#160;</td><td class="memItemRight" valign="bottom"><b>cGroupElem</b> (T &amp;concrete_obj)</td></tr>
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&#160;</td><td class="memItemRight" valign="bottom"><b>cGroupElem</b> (std::size_t size)</td></tr>
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&#160;</td><td class="memItemRight" valign="bottom"><b>cGroupElem</b> (const T &amp;concrete_obj)</td></tr>
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&#160;</td><td class="memItemRight" valign="bottom"><b>cGroupElem</b> (const std::initializer_list&lt; std::size_t &gt; &amp;perm_sq)</td></tr>
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&#160;</td><td class="memItemRight" valign="bottom"><b>cGroupElem</b> (std::size_t size, const std::initializer_list&lt; std::size_t &gt; &amp;perm_sq)</td></tr>
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&#160;</td><td class="memItemRight" valign="bottom"><b>cGroupElem</b> (const <a class="el" href="classcGroupElem.html">SelfType</a> &amp;group_elem)</td></tr>
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<a class="el" href="classcGroupElem.html">SelfType</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><b>operator=</b> (const <a class="el" href="classcGroupElem.html">SelfType</a> &amp;elem)</td></tr>
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<tr class="memitem:ac29fd7c4409752f596249999d87e64ca"><td class="memItemLeft" align="right" valign="top">std::size_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classcGroupElem.html#ac29fd7c4409752f596249999d87e64ca">GetOrder</a> () const </td></tr>
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<tr class="memitem:a17bf17389d7b17e8674ef33eabed9163"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classcGroupElem.html">SelfType</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classcGroupElem.html#a17bf17389d7b17e8674ef33eabed9163">GetInverse</a> () const </td></tr>
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<tr class="memitem:af58088ba8679e49a4b1a34b503a649e0"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classcGroupElem.html">SelfType</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classcGroupElem.html#af58088ba8679e49a4b1a34b503a649e0">GetNthPower</a> (std::size_t n) const </td></tr>
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<tr class="memitem:ab0e3d62bb8a37b59a371188f320bdbca"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classcGroupElem.html#ab0e3d62bb8a37b59a371188f320bdbca">CommutesWith</a> (const <a class="el" href="classcGroupElem.html">SelfType</a> &amp;element) const </td></tr>
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<tr class="memitem:ab01a807aff26daecd39cea6837b01e8e"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classcGroupElem.html#ab01a807aff26daecd39cea6837b01e8e">IsNormalizer</a> (const std::vector&lt; <a class="el" href="classcGroupElem.html">SelfType</a> &gt; &amp;elements) const </td></tr>
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<tr class="memitem:ae394d9b317db051ae804ae299f173e3d"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classcGroupElem.html">SelfType</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classcGroupElem.html#ae394d9b317db051ae804ae299f173e3d">GetIdentity</a> () const </td></tr>
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BinaryOp&#160;</td><td class="memItemRight" valign="bottom"><b>GetBinaryOp</b> () const </td></tr>
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Private Member Functions</h2></td></tr>
<tr class="memitem:a369cfffe505951aed65696857b25319b"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classcGroupElem.html">SelfType</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classcGroupElem.html#a369cfffe505951aed65696857b25319b">GetNthPower</a> (std::size_t n, const <a class="el" href="classcGroupElem.html">SelfType</a> &amp;element) const </td></tr>
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Private Attributes</h2></td></tr>
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BinaryOp&#160;</td><td class="memItemRight" valign="bottom"><b>m_BinOp</b></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template&lt;typename T, typename BinaryOp&gt;<br/>
class cGroupElem&lt; T, BinaryOp &gt;</h3>

<p>generic class that represents a group element must be instatiated with the concrete element type and the binary operation(used as a policy) that is going to used with the element </p>
</div><h2 class="groupheader">Member Function Documentation</h2>
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template&lt;typename T, typename BinaryOp&gt; </div>
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          <td class="memname">bool <a class="el" href="classcGroupElem.html">cGroupElem</a>&lt; T, BinaryOp &gt;::CommutesWith </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classcGroupElem.html">SelfType</a> &amp;&#160;</td>
          <td class="paramname"><em>element</em></td><td>)</td>
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<p>return true if the element commutes with the element given as parameter </p>

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template&lt;typename T, typename BinaryOp&gt; </div>
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          <td class="memname"><a class="el" href="classcGroupElem.html">SelfType</a> <a class="el" href="classcGroupElem.html">cGroupElem</a>&lt; T, BinaryOp &gt;::GetIdentity </td>
          <td>(</td>
          <td class="paramname"></td><td>)</td>
          <td> const</td>
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<p>returns the identity of the element type according to the binary operation </p>

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template&lt;typename T, typename BinaryOp&gt; </div>
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          <td class="memname"><a class="el" href="classcGroupElem.html">SelfType</a> <a class="el" href="classcGroupElem.html">cGroupElem</a>&lt; T, BinaryOp &gt;::GetInverse </td>
          <td>(</td>
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          <td> const</td>
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<p>returns the inverse of the element according to the given binaryu operation </p>

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template&lt;typename T, typename BinaryOp&gt; </div>
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          <td class="memname"><a class="el" href="classcGroupElem.html">SelfType</a> <a class="el" href="classcGroupElem.html">cGroupElem</a>&lt; T, BinaryOp &gt;::GetNthPower </td>
          <td>(</td>
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          <td class="paramname"><em>n</em></td><td>)</td>
          <td> const</td>
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<p>returns the nth power of the element </p>

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template&lt;typename T, typename BinaryOp&gt; </div>
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          <td class="memname"><a class="el" href="classcGroupElem.html">SelfType</a> <a class="el" href="classcGroupElem.html">cGroupElem</a>&lt; T, BinaryOp &gt;::GetNthPower </td>
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          <td></td>
          <td class="paramtype">const <a class="el" href="classcGroupElem.html">SelfType</a> &amp;&#160;</td>
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<p>recursive function that actually computes the nth power Complexity: <img class="formulaInl" alt="$ O(log_2(n)) $" src="form_0.png"/> </p>

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Here is the call graph for this function:</div>
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<div class="center"><img src="classcGroupElem_a369cfffe505951aed65696857b25319b_cgraph.png" border="0" usemap="#classcGroupElem_a369cfffe505951aed65696857b25319b_cgraph" alt=""/></div>
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<p>returns the identity element corresponding to the given element type and the binary operation Complexity: O(n) multiplications and comparisons, where n is the order </p>

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template&lt;typename T, typename BinaryOp&gt; </div>
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<p>returns the identity element corresponding to the given element type and the binary operation using the given group order Complexity: O(n) multiplication and d comparisons, where n is the order, and d is the number of divisors of the order of the group </p>

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template&lt;typename T, typename BinaryOp&gt; </div>
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          <td class="paramtype">const std::vector&lt; <a class="el" href="classcGroupElem.html">SelfType</a> &gt; &amp;&#160;</td>
          <td class="paramname"><em>elements</em></td><td>)</td>
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<p>returns true if the element is a normalizer for the list of elements given as parameter </p>

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<hr/>The documentation for this class was generated from the following file:<ul>
<li><a class="el" href="group__elem_8h_source.html">group_elem.h</a></li>
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